BOOK IIIJ OF NATURAL PHILOSOPHY. 415 respectively during the times in which the satellite and our moon (after parting from) are revolved (again) to the sun, by the same Corollary ; and therefore in the outmost satellite the variation does not exceed 5" 12'". PROPOSITION XXIV. THEOREM XIX. That the flax and reflux of the sea arise from the actions oj the sun and moon. By Cor. 19 and 20, Prop. LXVI, Book I, it appears that the waters of the sea ought twice to rise and twice to fall every day. as well lunar as solar ; and that the greatest height of the waters in the open and deep seas ought to follow the appulse of the luminaries to the meridian of the place by a less interval than 6 hours ; as happens in all that eastern tract of the Atlantic and jEthinpic seas between France and the Cape of Good Hope ; and on the coasts of Chili and Pern, in the Smith Sea ; in all which shores the ilo >d falls out about the second, third, or fourth hour, unless where the motion' propagated from the deep ocean is by the shallowness of the chaiir nels, through which it passes to some particular places, retarded to the fifth, sixth, or seventh hour, and even later. The hours I reckon from the appulse of each luminary to the meridian of the place, as well under as above the horizon ; and by the hours of the lunar day I understand the 24th parts uf that time which the moon, by its apparent diurnal motion, employs to come about again to the meridian of the place which it left the day before. The force of the sun or moon in raising the sea is greatest in the appulse of the luminary to the meridian of the place; but the force impressed upon the sea at that time continues a little while after the im pression, and is afterwards increased by a new though less force still act ing upon it. This makes the sea rise higher and higher, till this new force becoming too weak to raise it any more, the sea rises to its greatest height. And this will come to pass, perhaps, in one or two hours, but more fre quently near the shores in about three hours, or even more, where the sea is shallow. The two luminaries excite two motions, wrhich will not appear distinctly, but between them will arise one mixed motion compounded out of both. In the conjunction or opposition of the luminaries their forces will be con joined, and bring on the greatest flood and ebb. In the quadratures the sun will raise the waters which the moon depresses, and depress the waters which the moon raises, and from the difference of their forces the smallest of all tides will follow. And because (as experience tells us) the force of the moon is greater than that of the sun, the greatest height of the waters will happen about the third lunar hour. Out of the syzygies and quadra tures, the greatest tide, which by the single force of the moon oujjht to fall out at the third lunar hour, and by the single force of the sun at the third solar hour, by the compounded forces of both must fall out in an interme